Question

Four spheres of uniform density and having masses 1 kg, 2kg, 3 kg and 4 kg are placed at 1m, 2m, 3m, 4m along x-axis from origin.What is position of center of mass from origin.​

Answer 1

Answer :

Four sphere of masses 1kg, 2kg, 3kg and 4kg are placed at 1m, 2m, 3m and 4m along x-axis.

We have to find position of centre of mass from origin$.$

★ Centre of mass is a point which represents the mean position of the matter in a system.

• The COM of mass depends upon the consistent masses and their relative distribution. Any choice of reference frame will give the same position for the COM.

$:\implies\sf \: x_{CM}= \sum\limits^{n} _{i = 1} \bigg( \dfrac{m_ix_i}{m_i}\bigg)$

$:\implies\sf\:x_{CM}=\dfrac{m_1x_1+\dots+m_4x_4}{m_1+\dots+m_4}$

$:\implies\sf\:x_{CM}=\dfrac{1(1)+2(2)+3(3)+4(4)}{1+2+3+4}$

$:\implies\sf\:x_{CM}=\dfrac{1+4+9+16}{10}$

$:\implies\sf\:x_{CM}=\dfrac{30}{10}$

$:\implies\:\boxed{\bf{\red{x_{CM}=3\:cm}}}$